None of this is hard. Cruise ships with large numbers of Lesbian and Gay couples show up all the time. I can only suspect that they organize themselves through virtual methods or certain travel agencies market itineraries to them.
The easiest way to make this work might just come down to a few members agreeing on a port of departure and itinerary, and then just deciding to book cabins. Make an announcement of the details and other members can get their own cabins as they wish. No one is stuck trying to hold money, work the logistics of chartering a yacht, or all the other crap that comes with something of this scale.
Cruise travel is still way down and prices are really cheap at the moment. Ships pull into a day stop at Nassau probably not even 3/4 full, so there is capacity.
A cruise is going to be a lot cheaper, and in some ways just as inclusive, as a stay at a resort.